- FindStat

Identifier
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
Mp00125: Posets —dual poset⟶ Posets
Images
=>
            
              Cc0014;cc-rep-2Cc0014;cc-rep-3
            

            [1]=>[1]=>([],1)=>([],1)
[1,2]=>[1,2]=>([(0,1)],2)=>([(0,1)],2)
[2,1]=>[2,1]=>([(0,1)],2)=>([(0,1)],2)
[1,2,3]=>[1,2,3]=>([(0,2),(2,1)],3)=>([(0,2),(2,1)],3)
[1,3,2]=>[1,3,2]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,3),(2,3)],4)
[2,1,3]=>[2,1,3]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,3),(2,3)],4)
[2,3,1]=>[3,2,1]=>([(0,2),(2,1)],3)=>([(0,2),(2,1)],3)
[3,1,2]=>[3,1,2]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,3),(2,3)],4)
[3,2,1]=>[2,3,1]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,3),(2,3)],4)
[1,2,3,4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>([(0,3),(2,1),(3,2)],4)
[1,2,4,3]=>[1,2,4,3]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[1,3,2,4]=>[1,3,2,4]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
[1,3,4,2]=>[1,4,3,2]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[1,4,2,3]=>[1,4,2,3]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
[1,4,3,2]=>[1,3,4,2]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
[2,1,3,4]=>[2,1,3,4]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[2,1,4,3]=>[2,1,4,3]=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[2,3,1,4]=>[3,2,1,4]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[2,3,4,1]=>[4,2,3,1]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
[2,4,1,3]=>[4,2,1,3]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
[2,4,3,1]=>[3,2,4,1]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
[3,1,2,4]=>[3,1,2,4]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
[3,1,4,2]=>[3,4,1,2]=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[3,2,1,4]=>[2,3,1,4]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
[3,2,4,1]=>[4,3,2,1]=>([(0,3),(2,1),(3,2)],4)=>([(0,3),(2,1),(3,2)],4)
[3,4,1,2]=>[4,1,3,2]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
[3,4,2,1]=>[2,4,3,1]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
[4,1,2,3]=>[4,1,2,3]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[4,1,3,2]=>[4,3,1,2]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[4,2,3,1]=>[3,4,2,1]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[4,3,2,1]=>[2,3,4,1]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[1,2,3,4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,4),(2,3),(3,1),(4,2)],5)
[1,2,3,5,4]=>[1,2,3,5,4]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
[1,2,4,5,3]=>[1,2,5,4,3]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
[1,4,3,5,2]=>[1,5,4,3,2]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
[2,1,3,4,5]=>[2,1,3,4,5]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
[2,3,1,4,5]=>[3,2,1,4,5]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
[3,2,4,1,5]=>[4,3,2,1,5]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
[3,4,2,5,1]=>[5,4,3,2,1]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,4),(2,3),(3,1),(4,2)],5)
[3,5,1,4,2]=>[5,4,3,1,2]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
[3,5,2,4,1]=>[4,5,3,2,1]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
[4,3,1,5,2]=>[3,4,5,2,1]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
[5,4,3,2,1]=>[2,3,4,5,1]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>([(0,3),(0,4),(0,5),(1,13),(2,6),(2,7),(2,14),(3,9),(3,10),(4,9),(4,11),(5,2),(5,10),(5,11),(6,12),(7,12),(7,13),(9,1),(9,14),(10,6),(10,14),(11,7),(11,14),(12,8),(13,8),(14,12),(14,13)],15)=>([(0,3),(0,4),(1,9),(1,14),(2,10),(3,1),(3,7),(3,11),(4,2),(4,7),(4,11),(5,13),(6,13),(7,8),(7,14),(8,5),(8,12),(9,6),(9,12),(10,5),(10,6),(11,8),(11,9),(11,10),(11,14),(12,13),(14,12)],15)
[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,18),(1,19),(2,10),(2,13),(2,19),(2,20),(3,9),(3,13),(3,18),(3,20),(4,12),(4,14),(4,18),(4,19),(4,20),(5,11),(5,14),(5,18),(5,19),(5,20),(6,8),(6,9),(6,10),(6,11),(6,12),(8,21),(8,22),(9,15),(9,21),(9,25),(10,15),(10,22),(10,25),(11,16),(11,21),(11,22),(11,25),(12,16),(12,21),(12,22),(12,25),(13,15),(13,25),(14,16),(14,17),(14,25),(15,24),(16,23),(16,24),(17,23),(18,17),(18,21),(18,25),(19,17),(19,22),(19,25),(20,17),(20,25),(21,23),(21,24),(22,23),(22,24),(23,7),(24,7),(25,23),(25,24)],26)=>([(0,3),(0,4),(1,7),(1,13),(1,14),(2,8),(2,15),(2,16),(2,17),(3,1),(3,6),(3,9),(3,10),(3,11),(4,2),(4,6),(4,9),(4,10),(4,11),(5,12),(5,22),(6,15),(6,18),(6,19),(7,20),(7,21),(8,20),(8,21),(8,23),(8,24),(9,5),(9,14),(9,17),(9,18),(9,19),(10,5),(10,13),(10,16),(10,18),(10,19),(11,7),(11,8),(11,13),(11,14),(11,15),(11,16),(11,17),(11,18),(11,19),(12,25),(13,20),(13,22),(14,21),(14,22),(15,23),(15,24),(16,12),(16,20),(16,23),(16,24),(17,12),(17,21),(17,23),(17,24),(18,22),(18,24),(19,22),(19,23),(20,25),(21,25),(22,25),(23,25),(24,25)],26)
[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>([(0,3),(0,4),(0,5),(1,14),(2,6),(2,7),(3,9),(3,10),(4,9),(4,11),(5,2),(5,10),(5,11),(6,13),(7,13),(7,14),(9,1),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(12,14),(13,8),(14,8)],15)=>([(0,3),(0,4),(1,10),(2,7),(2,9),(3,2),(3,11),(3,12),(4,1),(4,11),(4,12),(5,14),(6,14),(7,13),(8,5),(8,13),(9,6),(9,13),(10,5),(10,6),(11,7),(11,8),(12,8),(12,9),(12,10),(13,14)],15)
[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>([(0,1),(0,2),(0,3),(1,5),(1,6),(1,12),(2,6),(2,7),(2,12),(3,5),(3,7),(3,12),(5,9),(5,10),(6,9),(6,11),(7,9),(7,10),(7,11),(8,4),(9,13),(10,8),(10,13),(11,8),(11,13),(12,10),(12,11),(13,4)],14)=>([(0,2),(0,3),(1,4),(1,5),(1,10),(2,7),(2,8),(3,1),(3,7),(3,8),(4,9),(4,12),(5,9),(5,11),(6,9),(6,11),(6,12),(7,5),(7,6),(7,10),(8,4),(8,6),(8,10),(9,13),(10,11),(10,12),(11,13),(12,13)],14)
[2,1,5,3,6,4]=>[2,1,5,6,3,4]=>([(0,2),(0,3),(0,4),(1,7),(1,8),(2,1),(2,11),(2,12),(3,9),(3,10),(3,12),(4,9),(4,10),(4,11),(5,15),(5,16),(7,15),(7,16),(8,15),(8,16),(9,5),(9,13),(10,5),(10,14),(11,7),(11,13),(11,14),(12,8),(12,13),(12,14),(13,16),(14,15),(14,16),(15,6),(16,6)],17)=>([(0,2),(0,3),(1,6),(1,11),(1,12),(2,7),(2,8),(2,9),(2,10),(3,1),(3,7),(3,8),(3,9),(3,10),(4,13),(4,14),(5,15),(6,13),(6,14),(7,5),(7,12),(8,5),(8,11),(9,4),(9,11),(9,12),(10,4),(10,6),(11,13),(11,15),(12,14),(12,15),(13,16),(14,16),(15,16)],17)
[2,1,6,3,5,4]=>[2,1,6,5,3,4]=>([(0,3),(0,4),(0,5),(1,6),(1,9),(2,7),(2,8),(3,1),(3,11),(3,13),(4,2),(4,12),(4,13),(5,11),(5,12),(6,15),(7,16),(8,15),(8,16),(9,15),(9,16),(11,9),(11,14),(12,7),(12,14),(13,6),(13,8),(13,14),(14,15),(14,16),(15,10),(16,10)],17)=>([(0,3),(0,4),(1,7),(1,13),(2,6),(2,9),(3,2),(3,10),(3,11),(3,12),(4,1),(4,10),(4,11),(4,12),(5,16),(6,14),(7,15),(8,5),(8,15),(9,5),(9,14),(10,6),(10,13),(11,7),(11,8),(12,8),(12,9),(12,13),(13,14),(13,15),(14,16),(15,16)],17)
[2,1,6,4,5,3]=>[2,1,5,6,4,3]=>([(0,3),(0,4),(0,5),(1,6),(1,9),(2,7),(2,8),(3,1),(3,11),(3,13),(4,2),(4,12),(4,13),(5,11),(5,12),(6,15),(7,16),(8,15),(8,16),(9,15),(9,16),(11,9),(11,14),(12,7),(12,14),(13,6),(13,8),(13,14),(14,15),(14,16),(15,10),(16,10)],17)=>([(0,3),(0,4),(1,7),(1,13),(2,6),(2,9),(3,2),(3,10),(3,11),(3,12),(4,1),(4,10),(4,11),(4,12),(5,16),(6,14),(7,15),(8,5),(8,15),(9,5),(9,14),(10,6),(10,13),(11,7),(11,8),(12,8),(12,9),(12,13),(13,14),(13,15),(14,16),(15,16)],17)
[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>([(0,3),(0,4),(0,5),(1,14),(2,6),(2,7),(3,9),(3,10),(4,9),(4,11),(5,2),(5,10),(5,11),(6,13),(7,13),(7,14),(9,1),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(12,14),(13,8),(14,8)],15)=>([(0,3),(0,4),(1,10),(2,7),(2,9),(3,2),(3,11),(3,12),(4,1),(4,11),(4,12),(5,14),(6,14),(7,13),(8,5),(8,13),(9,6),(9,13),(10,5),(10,6),(11,7),(11,8),(12,8),(12,9),(12,10),(13,14)],15)
[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>([(0,3),(0,4),(0,5),(1,13),(2,6),(2,7),(2,14),(3,9),(3,10),(4,9),(4,11),(5,2),(5,10),(5,11),(6,12),(7,12),(7,13),(9,1),(9,14),(10,6),(10,14),(11,7),(11,14),(12,8),(13,8),(14,12),(14,13)],15)=>([(0,3),(0,4),(1,9),(1,14),(2,10),(3,1),(3,7),(3,11),(4,2),(4,7),(4,11),(5,13),(6,13),(7,8),(7,14),(8,5),(8,12),(9,6),(9,12),(10,5),(10,6),(11,8),(11,9),(11,10),(11,14),(12,13),(14,12)],15)
[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)=>([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
[2,3,1,6,4,5]=>[3,2,1,6,4,5]=>([(0,3),(0,4),(0,6),(1,14),(2,14),(2,15),(3,8),(3,12),(4,9),(4,12),(5,2),(5,10),(5,11),(6,5),(6,8),(6,9),(8,11),(8,13),(9,10),(9,13),(10,15),(11,14),(11,15),(12,1),(12,13),(13,14),(13,15),(14,7),(15,7)],16)=>([(0,3),(0,4),(1,10),(1,15),(2,11),(3,1),(3,7),(3,8),(3,12),(4,2),(4,7),(4,8),(4,12),(5,14),(6,14),(7,15),(8,9),(8,15),(9,5),(9,13),(10,6),(10,13),(11,5),(11,6),(12,9),(12,10),(12,11),(13,14),(15,13)],16)
[2,3,1,6,5,4]=>[3,2,1,5,6,4]=>([(0,3),(0,4),(0,6),(1,14),(2,14),(2,15),(3,8),(3,12),(4,9),(4,12),(5,2),(5,10),(5,11),(6,5),(6,8),(6,9),(8,11),(8,13),(9,10),(9,13),(10,15),(11,14),(11,15),(12,1),(12,13),(13,14),(13,15),(14,7),(15,7)],16)=>([(0,3),(0,4),(1,10),(1,15),(2,11),(3,1),(3,7),(3,8),(3,12),(4,2),(4,7),(4,8),(4,12),(5,14),(6,14),(7,15),(8,9),(8,15),(9,5),(9,13),(10,6),(10,13),(11,5),(11,6),(12,9),(12,10),(12,11),(13,14),(15,13)],16)
[2,4,1,5,3,6]=>[4,2,5,1,3,6]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,18),(1,19),(2,10),(2,13),(2,19),(2,20),(3,9),(3,13),(3,18),(3,20),(4,12),(4,14),(4,18),(4,19),(4,20),(5,11),(5,14),(5,18),(5,19),(5,20),(6,8),(6,9),(6,10),(6,11),(6,12),(8,21),(8,22),(9,15),(9,21),(9,25),(10,15),(10,22),(10,25),(11,16),(11,21),(11,22),(11,25),(12,16),(12,21),(12,22),(12,25),(13,15),(13,25),(14,16),(14,17),(14,25),(15,24),(16,23),(16,24),(17,23),(18,17),(18,21),(18,25),(19,17),(19,22),(19,25),(20,17),(20,25),(21,23),(21,24),(22,23),(22,24),(23,7),(24,7),(25,23),(25,24)],26)=>([(0,3),(0,4),(1,7),(1,13),(1,14),(2,8),(2,15),(2,16),(2,17),(3,1),(3,6),(3,9),(3,10),(3,11),(4,2),(4,6),(4,9),(4,10),(4,11),(5,12),(5,22),(6,15),(6,18),(6,19),(7,20),(7,21),(8,20),(8,21),(8,23),(8,24),(9,5),(9,14),(9,17),(9,18),(9,19),(10,5),(10,13),(10,16),(10,18),(10,19),(11,7),(11,8),(11,13),(11,14),(11,15),(11,16),(11,17),(11,18),(11,19),(12,25),(13,20),(13,22),(14,21),(14,22),(15,23),(15,24),(16,12),(16,20),(16,23),(16,24),(17,12),(17,21),(17,23),(17,24),(18,22),(18,24),(19,22),(19,23),(20,25),(21,25),(22,25),(23,25),(24,25)],26)
[2,4,1,5,6,3]=>[4,2,6,1,5,3]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(1,13),(1,16),(1,17),(2,9),(2,13),(2,15),(2,17),(3,12),(3,14),(3,15),(3,17),(4,11),(4,14),(4,16),(4,17),(5,8),(5,11),(5,12),(5,15),(5,16),(6,8),(6,9),(6,10),(6,15),(6,16),(8,19),(8,20),(9,19),(9,22),(9,23),(10,20),(10,22),(10,23),(11,19),(11,22),(11,24),(12,20),(12,22),(12,24),(13,22),(13,23),(14,22),(14,24),(15,19),(15,20),(15,23),(15,24),(16,19),(16,20),(16,23),(16,24),(17,23),(17,24),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,21),(23,18),(23,21),(24,18),(24,21)],25)=>([(0,2),(0,3),(1,5),(1,6),(1,12),(1,13),(1,14),(1,15),(2,8),(2,9),(2,10),(2,11),(3,1),(3,8),(3,9),(3,10),(3,11),(4,22),(4,23),(5,20),(5,21),(6,18),(6,19),(7,18),(7,19),(7,20),(7,21),(8,4),(8,13),(8,15),(8,16),(8,17),(9,4),(9,12),(9,14),(9,16),(9,17),(10,6),(10,7),(10,12),(10,13),(10,16),(10,17),(11,5),(11,7),(11,14),(11,15),(11,16),(11,17),(12,18),(12,22),(13,19),(13,22),(14,20),(14,23),(15,21),(15,23),(16,18),(16,21),(16,22),(16,23),(17,19),(17,20),(17,22),(17,23),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
[2,4,1,6,3,5]=>[4,2,6,1,3,5]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,18),(1,22),(2,11),(2,14),(2,16),(2,18),(3,9),(3,14),(3,15),(3,22),(4,12),(4,13),(4,16),(4,22),(5,10),(5,13),(5,15),(5,18),(5,22),(6,8),(6,10),(6,11),(6,12),(6,22),(8,20),(8,25),(9,19),(9,25),(10,20),(10,21),(10,25),(10,26),(11,17),(11,25),(11,26),(12,17),(12,20),(12,26),(13,21),(13,26),(14,19),(14,26),(15,19),(15,21),(15,25),(16,17),(16,26),(17,24),(18,19),(18,25),(18,26),(19,23),(20,23),(20,24),(21,23),(21,24),(22,20),(22,21),(22,25),(22,26),(23,7),(24,7),(25,23),(25,24),(26,23),(26,24)],27)=>([(0,3),(0,4),(1,6),(1,14),(1,17),(2,5),(2,9),(2,15),(2,16),(3,2),(3,10),(3,11),(3,12),(3,13),(4,1),(4,10),(4,11),(4,12),(4,13),(5,22),(5,23),(6,20),(6,23),(7,20),(7,24),(8,21),(8,25),(9,21),(9,22),(10,8),(10,17),(10,18),(10,19),(11,7),(11,16),(11,18),(11,19),(12,8),(12,9),(12,14),(12,15),(12,16),(12,18),(12,19),(13,5),(13,6),(13,7),(13,14),(13,15),(13,17),(13,18),(13,19),(14,23),(14,25),(15,21),(15,23),(15,24),(16,22),(16,24),(17,20),(17,25),(18,24),(18,25),(19,20),(19,21),(19,22),(19,24),(19,25),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
[2,4,1,6,5,3]=>[4,2,5,1,6,3]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,18),(1,22),(2,11),(2,14),(2,16),(2,18),(3,9),(3,14),(3,15),(3,22),(4,12),(4,13),(4,16),(4,22),(5,10),(5,13),(5,15),(5,18),(5,22),(6,8),(6,10),(6,11),(6,12),(6,22),(8,20),(8,25),(9,19),(9,25),(10,20),(10,21),(10,25),(10,26),(11,17),(11,25),(11,26),(12,17),(12,20),(12,26),(13,21),(13,26),(14,19),(14,26),(15,19),(15,21),(15,25),(16,17),(16,26),(17,24),(18,19),(18,25),(18,26),(19,23),(20,23),(20,24),(21,23),(21,24),(22,20),(22,21),(22,25),(22,26),(23,7),(24,7),(25,23),(25,24),(26,23),(26,24)],27)=>([(0,3),(0,4),(1,6),(1,14),(1,17),(2,5),(2,9),(2,15),(2,16),(3,2),(3,10),(3,11),(3,12),(3,13),(4,1),(4,10),(4,11),(4,12),(4,13),(5,22),(5,23),(6,20),(6,23),(7,20),(7,24),(8,21),(8,25),(9,21),(9,22),(10,8),(10,17),(10,18),(10,19),(11,7),(11,16),(11,18),(11,19),(12,8),(12,9),(12,14),(12,15),(12,16),(12,18),(12,19),(13,5),(13,6),(13,7),(13,14),(13,15),(13,17),(13,18),(13,19),(14,23),(14,25),(15,21),(15,23),(15,24),(16,22),(16,24),(17,20),(17,25),(18,24),(18,25),(19,20),(19,21),(19,22),(19,24),(19,25),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
[3,1,2,5,6,4]=>[3,1,2,6,5,4]=>([(0,3),(0,4),(0,6),(1,14),(2,14),(2,15),(3,8),(3,12),(4,9),(4,12),(5,2),(5,10),(5,11),(6,5),(6,8),(6,9),(8,11),(8,13),(9,10),(9,13),(10,15),(11,14),(11,15),(12,1),(12,13),(13,14),(13,15),(14,7),(15,7)],16)=>([(0,3),(0,4),(1,10),(1,15),(2,11),(3,1),(3,7),(3,8),(3,12),(4,2),(4,7),(4,8),(4,12),(5,14),(6,14),(7,15),(8,9),(8,15),(9,5),(9,13),(10,6),(10,13),(11,5),(11,6),(12,9),(12,10),(12,11),(13,14),(15,13)],16)
[3,1,4,2,6,5]=>[3,4,1,2,6,5]=>([(0,2),(0,3),(0,4),(1,7),(1,8),(2,1),(2,11),(2,12),(3,9),(3,10),(3,12),(4,9),(4,10),(4,11),(5,15),(5,16),(7,15),(7,16),(8,15),(8,16),(9,5),(9,13),(10,5),(10,14),(11,7),(11,13),(11,14),(12,8),(12,13),(12,14),(13,16),(14,15),(14,16),(15,6),(16,6)],17)=>([(0,2),(0,3),(1,6),(1,11),(1,12),(2,7),(2,8),(2,9),(2,10),(3,1),(3,7),(3,8),(3,9),(3,10),(4,13),(4,14),(5,15),(6,13),(6,14),(7,5),(7,12),(8,5),(8,11),(9,4),(9,11),(9,12),(10,4),(10,6),(11,13),(11,15),(12,14),(12,15),(13,16),(14,16),(15,16)],17)
[3,1,5,2,6,4]=>[3,5,1,6,2,4]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(1,13),(1,16),(1,17),(2,9),(2,13),(2,15),(2,17),(3,12),(3,14),(3,15),(3,17),(4,11),(4,14),(4,16),(4,17),(5,8),(5,11),(5,12),(5,15),(5,16),(6,8),(6,9),(6,10),(6,15),(6,16),(8,19),(8,20),(9,19),(9,22),(9,23),(10,20),(10,22),(10,23),(11,19),(11,22),(11,24),(12,20),(12,22),(12,24),(13,22),(13,23),(14,22),(14,24),(15,19),(15,20),(15,23),(15,24),(16,19),(16,20),(16,23),(16,24),(17,23),(17,24),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,21),(23,18),(23,21),(24,18),(24,21)],25)=>([(0,2),(0,3),(1,5),(1,6),(1,12),(1,13),(1,14),(1,15),(2,8),(2,9),(2,10),(2,11),(3,1),(3,8),(3,9),(3,10),(3,11),(4,22),(4,23),(5,20),(5,21),(6,18),(6,19),(7,18),(7,19),(7,20),(7,21),(8,4),(8,13),(8,15),(8,16),(8,17),(9,4),(9,12),(9,14),(9,16),(9,17),(10,6),(10,7),(10,12),(10,13),(10,16),(10,17),(11,5),(11,7),(11,14),(11,15),(11,16),(11,17),(12,18),(12,22),(13,19),(13,22),(14,20),(14,23),(15,21),(15,23),(16,18),(16,21),(16,22),(16,23),(17,19),(17,20),(17,22),(17,23),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
[3,1,6,2,5,4]=>[3,6,1,5,2,4]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,18),(1,22),(2,11),(2,14),(2,16),(2,18),(3,9),(3,14),(3,15),(3,22),(4,12),(4,13),(4,16),(4,22),(5,10),(5,13),(5,15),(5,18),(5,22),(6,8),(6,10),(6,11),(6,12),(6,22),(8,20),(8,25),(9,19),(9,25),(10,20),(10,21),(10,25),(10,26),(11,17),(11,25),(11,26),(12,17),(12,20),(12,26),(13,21),(13,26),(14,19),(14,26),(15,19),(15,21),(15,25),(16,17),(16,26),(17,24),(18,19),(18,25),(18,26),(19,23),(20,23),(20,24),(21,23),(21,24),(22,20),(22,21),(22,25),(22,26),(23,7),(24,7),(25,23),(25,24),(26,23),(26,24)],27)=>([(0,3),(0,4),(1,6),(1,14),(1,17),(2,5),(2,9),(2,15),(2,16),(3,2),(3,10),(3,11),(3,12),(3,13),(4,1),(4,10),(4,11),(4,12),(4,13),(5,22),(5,23),(6,20),(6,23),(7,20),(7,24),(8,21),(8,25),(9,21),(9,22),(10,8),(10,17),(10,18),(10,19),(11,7),(11,16),(11,18),(11,19),(12,8),(12,9),(12,14),(12,15),(12,16),(12,18),(12,19),(13,5),(13,6),(13,7),(13,14),(13,15),(13,17),(13,18),(13,19),(14,23),(14,25),(15,21),(15,23),(15,24),(16,22),(16,24),(17,20),(17,25),(18,24),(18,25),(19,20),(19,21),(19,22),(19,24),(19,25),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
[3,1,6,4,5,2]=>[3,5,1,6,4,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,18),(1,22),(2,11),(2,14),(2,16),(2,18),(3,9),(3,14),(3,15),(3,22),(4,12),(4,13),(4,16),(4,22),(5,10),(5,13),(5,15),(5,18),(5,22),(6,8),(6,10),(6,11),(6,12),(6,22),(8,20),(8,25),(9,19),(9,25),(10,20),(10,21),(10,25),(10,26),(11,17),(11,25),(11,26),(12,17),(12,20),(12,26),(13,21),(13,26),(14,19),(14,26),(15,19),(15,21),(15,25),(16,17),(16,26),(17,24),(18,19),(18,25),(18,26),(19,23),(20,23),(20,24),(21,23),(21,24),(22,20),(22,21),(22,25),(22,26),(23,7),(24,7),(25,23),(25,24),(26,23),(26,24)],27)=>([(0,3),(0,4),(1,6),(1,14),(1,17),(2,5),(2,9),(2,15),(2,16),(3,2),(3,10),(3,11),(3,12),(3,13),(4,1),(4,10),(4,11),(4,12),(4,13),(5,22),(5,23),(6,20),(6,23),(7,20),(7,24),(8,21),(8,25),(9,21),(9,22),(10,8),(10,17),(10,18),(10,19),(11,7),(11,16),(11,18),(11,19),(12,8),(12,9),(12,14),(12,15),(12,16),(12,18),(12,19),(13,5),(13,6),(13,7),(13,14),(13,15),(13,17),(13,18),(13,19),(14,23),(14,25),(15,21),(15,23),(15,24),(16,22),(16,24),(17,20),(17,25),(18,24),(18,25),(19,20),(19,21),(19,22),(19,24),(19,25),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
[3,2,1,5,6,4]=>[2,3,1,6,5,4]=>([(0,3),(0,4),(0,6),(1,14),(2,14),(2,15),(3,8),(3,12),(4,9),(4,12),(5,2),(5,10),(5,11),(6,5),(6,8),(6,9),(8,11),(8,13),(9,10),(9,13),(10,15),(11,14),(11,15),(12,1),(12,13),(13,14),(13,15),(14,7),(15,7)],16)=>([(0,3),(0,4),(1,10),(1,15),(2,11),(3,1),(3,7),(3,8),(3,12),(4,2),(4,7),(4,8),(4,12),(5,14),(6,14),(7,15),(8,9),(8,15),(9,5),(9,13),(10,6),(10,13),(11,5),(11,6),(12,9),(12,10),(12,11),(13,14),(15,13)],16)
[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
[3,4,5,1,6,2]=>[5,6,3,4,1,2]=>([(0,1),(0,2),(0,3),(1,5),(1,6),(1,12),(2,6),(2,7),(2,12),(3,5),(3,7),(3,12),(5,9),(5,10),(6,9),(6,11),(7,9),(7,10),(7,11),(8,4),(9,13),(10,8),(10,13),(11,8),(11,13),(12,10),(12,11),(13,4)],14)=>([(0,2),(0,3),(1,4),(1,5),(1,10),(2,7),(2,8),(3,1),(3,7),(3,8),(4,9),(4,12),(5,9),(5,11),(6,9),(6,11),(6,12),(7,5),(7,6),(7,10),(8,4),(8,6),(8,10),(9,13),(10,11),(10,12),(11,13),(12,13)],14)
[4,1,2,5,6,3]=>[4,1,6,2,5,3]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,18),(1,22),(2,11),(2,14),(2,16),(2,18),(3,9),(3,14),(3,15),(3,22),(4,12),(4,13),(4,16),(4,22),(5,10),(5,13),(5,15),(5,18),(5,22),(6,8),(6,10),(6,11),(6,12),(6,22),(8,20),(8,25),(9,19),(9,25),(10,20),(10,21),(10,25),(10,26),(11,17),(11,25),(11,26),(12,17),(12,20),(12,26),(13,21),(13,26),(14,19),(14,26),(15,19),(15,21),(15,25),(16,17),(16,26),(17,24),(18,19),(18,25),(18,26),(19,23),(20,23),(20,24),(21,23),(21,24),(22,20),(22,21),(22,25),(22,26),(23,7),(24,7),(25,23),(25,24),(26,23),(26,24)],27)=>([(0,3),(0,4),(1,6),(1,14),(1,17),(2,5),(2,9),(2,15),(2,16),(3,2),(3,10),(3,11),(3,12),(3,13),(4,1),(4,10),(4,11),(4,12),(4,13),(5,22),(5,23),(6,20),(6,23),(7,20),(7,24),(8,21),(8,25),(9,21),(9,22),(10,8),(10,17),(10,18),(10,19),(11,7),(11,16),(11,18),(11,19),(12,8),(12,9),(12,14),(12,15),(12,16),(12,18),(12,19),(13,5),(13,6),(13,7),(13,14),(13,15),(13,17),(13,18),(13,19),(14,23),(14,25),(15,21),(15,23),(15,24),(16,22),(16,24),(17,20),(17,25),(18,24),(18,25),(19,20),(19,21),(19,22),(19,24),(19,25),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
[4,1,3,2,6,5]=>[4,3,1,2,6,5]=>([(0,3),(0,4),(0,5),(1,6),(1,9),(2,7),(2,8),(3,1),(3,11),(3,13),(4,2),(4,12),(4,13),(5,11),(5,12),(6,15),(7,16),(8,15),(8,16),(9,15),(9,16),(11,9),(11,14),(12,7),(12,14),(13,6),(13,8),(13,14),(14,15),(14,16),(15,10),(16,10)],17)=>([(0,3),(0,4),(1,7),(1,13),(2,6),(2,9),(3,2),(3,10),(3,11),(3,12),(4,1),(4,10),(4,11),(4,12),(5,16),(6,14),(7,15),(8,5),(8,15),(9,5),(9,14),(10,6),(10,13),(11,7),(11,8),(12,8),(12,9),(12,13),(13,14),(13,15),(14,16),(15,16)],17)
[4,1,5,2,6,3]=>[4,5,6,1,2,3]=>([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)=>([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
[4,1,6,2,5,3]=>[4,6,5,1,2,3]=>([(0,3),(0,4),(0,6),(1,14),(2,14),(2,15),(3,8),(3,12),(4,9),(4,12),(5,2),(5,10),(5,11),(6,5),(6,8),(6,9),(8,11),(8,13),(9,10),(9,13),(10,15),(11,14),(11,15),(12,1),(12,13),(13,14),(13,15),(14,7),(15,7)],16)=>([(0,3),(0,4),(1,10),(1,15),(2,11),(3,1),(3,7),(3,8),(3,12),(4,2),(4,7),(4,8),(4,12),(5,14),(6,14),(7,15),(8,9),(8,15),(9,5),(9,13),(10,6),(10,13),(11,5),(11,6),(12,9),(12,10),(12,11),(13,14),(15,13)],16)
[4,1,6,3,5,2]=>[4,5,6,1,3,2]=>([(0,3),(0,4),(0,6),(1,14),(2,14),(2,15),(3,8),(3,12),(4,9),(4,12),(5,2),(5,10),(5,11),(6,5),(6,8),(6,9),(8,11),(8,13),(9,10),(9,13),(10,15),(11,14),(11,15),(12,1),(12,13),(13,14),(13,15),(14,7),(15,7)],16)=>([(0,3),(0,4),(1,10),(1,15),(2,11),(3,1),(3,7),(3,8),(3,12),(4,2),(4,7),(4,8),(4,12),(5,14),(6,14),(7,15),(8,9),(8,15),(9,5),(9,13),(10,6),(10,13),(11,5),(11,6),(12,9),(12,10),(12,11),(13,14),(15,13)],16)
[4,2,1,5,6,3]=>[2,4,6,1,5,3]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,18),(1,22),(2,11),(2,14),(2,16),(2,18),(3,9),(3,14),(3,15),(3,22),(4,12),(4,13),(4,16),(4,22),(5,10),(5,13),(5,15),(5,18),(5,22),(6,8),(6,10),(6,11),(6,12),(6,22),(8,20),(8,25),(9,19),(9,25),(10,20),(10,21),(10,25),(10,26),(11,17),(11,25),(11,26),(12,17),(12,20),(12,26),(13,21),(13,26),(14,19),(14,26),(15,19),(15,21),(15,25),(16,17),(16,26),(17,24),(18,19),(18,25),(18,26),(19,23),(20,23),(20,24),(21,23),(21,24),(22,20),(22,21),(22,25),(22,26),(23,7),(24,7),(25,23),(25,24),(26,23),(26,24)],27)=>([(0,3),(0,4),(1,6),(1,14),(1,17),(2,5),(2,9),(2,15),(2,16),(3,2),(3,10),(3,11),(3,12),(3,13),(4,1),(4,10),(4,11),(4,12),(4,13),(5,22),(5,23),(6,20),(6,23),(7,20),(7,24),(8,21),(8,25),(9,21),(9,22),(10,8),(10,17),(10,18),(10,19),(11,7),(11,16),(11,18),(11,19),(12,8),(12,9),(12,14),(12,15),(12,16),(12,18),(12,19),(13,5),(13,6),(13,7),(13,14),(13,15),(13,17),(13,18),(13,19),(14,23),(14,25),(15,21),(15,23),(15,24),(16,22),(16,24),(17,20),(17,25),(18,24),(18,25),(19,20),(19,21),(19,22),(19,24),(19,25),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
[4,2,3,1,6,5]=>[3,4,2,1,6,5]=>([(0,3),(0,4),(0,5),(1,6),(1,9),(2,7),(2,8),(3,1),(3,11),(3,13),(4,2),(4,12),(4,13),(5,11),(5,12),(6,15),(7,16),(8,15),(8,16),(9,15),(9,16),(11,9),(11,14),(12,7),(12,14),(13,6),(13,8),(13,14),(14,15),(14,16),(15,10),(16,10)],17)=>([(0,3),(0,4),(1,7),(1,13),(2,6),(2,9),(3,2),(3,10),(3,11),(3,12),(4,1),(4,10),(4,11),(4,12),(5,16),(6,14),(7,15),(8,5),(8,15),(9,5),(9,14),(10,6),(10,13),(11,7),(11,8),(12,8),(12,9),(12,13),(13,14),(13,15),(14,16),(15,16)],17)
[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[4,3,6,1,5,2]=>[6,5,4,3,1,2]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
[4,3,6,2,5,1]=>[5,6,4,3,2,1]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
[5,1,3,2,6,4]=>[5,3,1,6,2,4]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,18),(1,22),(2,11),(2,14),(2,16),(2,18),(3,9),(3,14),(3,15),(3,22),(4,12),(4,13),(4,16),(4,22),(5,10),(5,13),(5,15),(5,18),(5,22),(6,8),(6,10),(6,11),(6,12),(6,22),(8,20),(8,25),(9,19),(9,25),(10,20),(10,21),(10,25),(10,26),(11,17),(11,25),(11,26),(12,17),(12,20),(12,26),(13,21),(13,26),(14,19),(14,26),(15,19),(15,21),(15,25),(16,17),(16,26),(17,24),(18,19),(18,25),(18,26),(19,23),(20,23),(20,24),(21,23),(21,24),(22,20),(22,21),(22,25),(22,26),(23,7),(24,7),(25,23),(25,24),(26,23),(26,24)],27)=>([(0,3),(0,4),(1,6),(1,14),(1,17),(2,5),(2,9),(2,15),(2,16),(3,2),(3,10),(3,11),(3,12),(3,13),(4,1),(4,10),(4,11),(4,12),(4,13),(5,22),(5,23),(6,20),(6,23),(7,20),(7,24),(8,21),(8,25),(9,21),(9,22),(10,8),(10,17),(10,18),(10,19),(11,7),(11,16),(11,18),(11,19),(12,8),(12,9),(12,14),(12,15),(12,16),(12,18),(12,19),(13,5),(13,6),(13,7),(13,14),(13,15),(13,17),(13,18),(13,19),(14,23),(14,25),(15,21),(15,23),(15,24),(16,22),(16,24),(17,20),(17,25),(18,24),(18,25),(19,20),(19,21),(19,22),(19,24),(19,25),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
[5,1,4,2,6,3]=>[5,4,6,1,2,3]=>([(0,3),(0,4),(0,6),(1,14),(2,14),(2,15),(3,8),(3,12),(4,9),(4,12),(5,2),(5,10),(5,11),(6,5),(6,8),(6,9),(8,11),(8,13),(9,10),(9,13),(10,15),(11,14),(11,15),(12,1),(12,13),(13,14),(13,15),(14,7),(15,7)],16)=>([(0,3),(0,4),(1,10),(1,15),(2,11),(3,1),(3,7),(3,8),(3,12),(4,2),(4,7),(4,8),(4,12),(5,14),(6,14),(7,15),(8,9),(8,15),(9,5),(9,13),(10,6),(10,13),(11,5),(11,6),(12,9),(12,10),(12,11),(13,14),(15,13)],16)
[5,1,4,6,2,3]=>[5,6,2,1,4,3]=>([(0,2),(0,3),(0,4),(1,7),(1,8),(2,1),(2,11),(2,12),(3,9),(3,10),(3,12),(4,9),(4,10),(4,11),(5,15),(5,16),(7,15),(7,16),(8,15),(8,16),(9,5),(9,13),(10,5),(10,14),(11,7),(11,13),(11,14),(12,8),(12,13),(12,14),(13,16),(14,15),(14,16),(15,6),(16,6)],17)=>([(0,2),(0,3),(1,6),(1,11),(1,12),(2,7),(2,8),(2,9),(2,10),(3,1),(3,7),(3,8),(3,9),(3,10),(4,13),(4,14),(5,15),(6,13),(6,14),(7,5),(7,12),(8,5),(8,11),(9,4),(9,11),(9,12),(10,4),(10,6),(11,13),(11,15),(12,14),(12,15),(13,16),(14,16),(15,16)],17)
[5,2,3,1,6,4]=>[3,5,2,6,1,4]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,18),(1,22),(2,11),(2,14),(2,16),(2,18),(3,9),(3,14),(3,15),(3,22),(4,12),(4,13),(4,16),(4,22),(5,10),(5,13),(5,15),(5,18),(5,22),(6,8),(6,10),(6,11),(6,12),(6,22),(8,20),(8,25),(9,19),(9,25),(10,20),(10,21),(10,25),(10,26),(11,17),(11,25),(11,26),(12,17),(12,20),(12,26),(13,21),(13,26),(14,19),(14,26),(15,19),(15,21),(15,25),(16,17),(16,26),(17,24),(18,19),(18,25),(18,26),(19,23),(20,23),(20,24),(21,23),(21,24),(22,20),(22,21),(22,25),(22,26),(23,7),(24,7),(25,23),(25,24),(26,23),(26,24)],27)=>([(0,3),(0,4),(1,6),(1,14),(1,17),(2,5),(2,9),(2,15),(2,16),(3,2),(3,10),(3,11),(3,12),(3,13),(4,1),(4,10),(4,11),(4,12),(4,13),(5,22),(5,23),(6,20),(6,23),(7,20),(7,24),(8,21),(8,25),(9,21),(9,22),(10,8),(10,17),(10,18),(10,19),(11,7),(11,16),(11,18),(11,19),(12,8),(12,9),(12,14),(12,15),(12,16),(12,18),(12,19),(13,5),(13,6),(13,7),(13,14),(13,15),(13,17),(13,18),(13,19),(14,23),(14,25),(15,21),(15,23),(15,24),(16,22),(16,24),(17,20),(17,25),(18,24),(18,25),(19,20),(19,21),(19,22),(19,24),(19,25),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
[5,2,4,1,6,3]=>[4,5,6,2,1,3]=>([(0,3),(0,4),(0,6),(1,14),(2,14),(2,15),(3,8),(3,12),(4,9),(4,12),(5,2),(5,10),(5,11),(6,5),(6,8),(6,9),(8,11),(8,13),(9,10),(9,13),(10,15),(11,14),(11,15),(12,1),(12,13),(13,14),(13,15),(14,7),(15,7)],16)=>([(0,3),(0,4),(1,10),(1,15),(2,11),(3,1),(3,7),(3,8),(3,12),(4,2),(4,7),(4,8),(4,12),(5,14),(6,14),(7,15),(8,9),(8,15),(9,5),(9,13),(10,6),(10,13),(11,5),(11,6),(12,9),(12,10),(12,11),(13,14),(15,13)],16)
[5,2,6,1,4,3]=>[6,5,4,1,2,3]=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
[5,2,6,3,4,1]=>[4,5,6,3,2,1]=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
[5,3,2,6,4,1]=>[4,3,6,5,1,2]=>([(0,2),(0,3),(0,4),(1,7),(1,8),(2,1),(2,11),(2,12),(3,9),(3,10),(3,12),(4,9),(4,10),(4,11),(5,15),(5,16),(7,15),(7,16),(8,15),(8,16),(9,5),(9,13),(10,5),(10,14),(11,7),(11,13),(11,14),(12,8),(12,13),(12,14),(13,16),(14,15),(14,16),(15,6),(16,6)],17)=>([(0,2),(0,3),(1,6),(1,11),(1,12),(2,7),(2,8),(2,9),(2,10),(3,1),(3,7),(3,8),(3,9),(3,10),(4,13),(4,14),(5,15),(6,13),(6,14),(7,5),(7,12),(8,5),(8,11),(9,4),(9,11),(9,12),(10,4),(10,6),(11,13),(11,15),(12,14),(12,15),(13,16),(14,16),(15,16)],17)
[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
[6,1,3,2,5,4]=>[6,3,1,5,2,4]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,18),(1,19),(2,10),(2,13),(2,19),(2,20),(3,9),(3,13),(3,18),(3,20),(4,12),(4,14),(4,18),(4,19),(4,20),(5,11),(5,14),(5,18),(5,19),(5,20),(6,8),(6,9),(6,10),(6,11),(6,12),(8,21),(8,22),(9,15),(9,21),(9,25),(10,15),(10,22),(10,25),(11,16),(11,21),(11,22),(11,25),(12,16),(12,21),(12,22),(12,25),(13,15),(13,25),(14,16),(14,17),(14,25),(15,24),(16,23),(16,24),(17,23),(18,17),(18,21),(18,25),(19,17),(19,22),(19,25),(20,17),(20,25),(21,23),(21,24),(22,23),(22,24),(23,7),(24,7),(25,23),(25,24)],26)=>([(0,3),(0,4),(1,7),(1,13),(1,14),(2,8),(2,15),(2,16),(2,17),(3,1),(3,6),(3,9),(3,10),(3,11),(4,2),(4,6),(4,9),(4,10),(4,11),(5,12),(5,22),(6,15),(6,18),(6,19),(7,20),(7,21),(8,20),(8,21),(8,23),(8,24),(9,5),(9,14),(9,17),(9,18),(9,19),(10,5),(10,13),(10,16),(10,18),(10,19),(11,7),(11,8),(11,13),(11,14),(11,15),(11,16),(11,17),(11,18),(11,19),(12,25),(13,20),(13,22),(14,21),(14,22),(15,23),(15,24),(16,12),(16,20),(16,23),(16,24),(17,12),(17,21),(17,23),(17,24),(18,22),(18,24),(19,22),(19,23),(20,25),(21,25),(22,25),(23,25),(24,25)],26)
[6,1,3,5,2,4]=>[6,5,1,2,3,4]=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
[6,1,4,2,5,3]=>[6,4,5,1,2,3]=>([(0,3),(0,4),(0,5),(1,13),(2,6),(2,7),(2,14),(3,9),(3,10),(4,9),(4,11),(5,2),(5,10),(5,11),(6,12),(7,12),(7,13),(9,1),(9,14),(10,6),(10,14),(11,7),(11,14),(12,8),(13,8),(14,12),(14,13)],15)=>([(0,3),(0,4),(1,9),(1,14),(2,10),(3,1),(3,7),(3,11),(4,2),(4,7),(4,11),(5,13),(6,13),(7,8),(7,14),(8,5),(8,12),(9,6),(9,12),(10,5),(10,6),(11,8),(11,9),(11,10),(11,14),(12,13),(14,12)],15)
[6,2,3,5,1,4]=>[5,6,2,1,3,4]=>([(0,3),(0,4),(0,5),(1,6),(1,9),(2,7),(2,8),(3,1),(3,11),(3,13),(4,2),(4,12),(4,13),(5,11),(5,12),(6,15),(7,16),(8,15),(8,16),(9,15),(9,16),(11,9),(11,14),(12,7),(12,14),(13,6),(13,8),(13,14),(14,15),(14,16),(15,10),(16,10)],17)=>([(0,3),(0,4),(1,7),(1,13),(2,6),(2,9),(3,2),(3,10),(3,11),(3,12),(4,1),(4,10),(4,11),(4,12),(5,16),(6,14),(7,15),(8,5),(8,15),(9,5),(9,14),(10,6),(10,13),(11,7),(11,8),(12,8),(12,9),(12,13),(13,14),(13,15),(14,16),(15,16)],17)
[6,2,4,5,1,3]=>[5,6,1,2,4,3]=>([(0,3),(0,4),(0,5),(1,6),(1,9),(2,7),(2,8),(3,1),(3,11),(3,13),(4,2),(4,12),(4,13),(5,11),(5,12),(6,15),(7,16),(8,15),(8,16),(9,15),(9,16),(11,9),(11,14),(12,7),(12,14),(13,6),(13,8),(13,14),(14,15),(14,16),(15,10),(16,10)],17)=>([(0,3),(0,4),(1,7),(1,13),(2,6),(2,9),(3,2),(3,10),(3,11),(3,12),(4,1),(4,10),(4,11),(4,12),(5,16),(6,14),(7,15),(8,5),(8,15),(9,5),(9,14),(10,6),(10,13),(11,7),(11,8),(12,8),(12,9),(12,13),(13,14),(13,15),(14,16),(15,16)],17)
[6,2,5,1,4,3]=>[5,6,4,1,2,3]=>([(0,3),(0,4),(0,5),(1,14),(2,6),(2,7),(3,9),(3,10),(4,9),(4,11),(5,2),(5,10),(5,11),(6,13),(7,13),(7,14),(9,1),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(12,14),(13,8),(14,8)],15)=>([(0,3),(0,4),(1,10),(2,7),(2,9),(3,2),(3,11),(3,12),(4,1),(4,11),(4,12),(5,14),(6,14),(7,13),(8,5),(8,13),(9,6),(9,13),(10,5),(10,6),(11,7),(11,8),(12,8),(12,9),(12,10),(13,14)],15)
[6,2,5,4,3,1]=>[3,4,5,6,2,1]=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
[6,3,2,5,4,1]=>[4,3,5,6,1,2]=>([(0,3),(0,4),(0,5),(1,6),(1,9),(2,7),(2,8),(3,1),(3,11),(3,13),(4,2),(4,12),(4,13),(5,11),(5,12),(6,15),(7,16),(8,15),(8,16),(9,15),(9,16),(11,9),(11,14),(12,7),(12,14),(13,6),(13,8),(13,14),(14,15),(14,16),(15,10),(16,10)],17)=>([(0,3),(0,4),(1,7),(1,13),(2,6),(2,9),(3,2),(3,10),(3,11),(3,12),(4,1),(4,10),(4,11),(4,12),(5,16),(6,14),(7,15),(8,5),(8,15),(9,5),(9,14),(10,6),(10,13),(11,7),(11,8),(12,8),(12,9),(12,13),(13,14),(13,15),(14,16),(15,16)],17)
[6,3,4,1,5,2]=>[4,5,6,3,1,2]=>([(0,3),(0,4),(0,5),(1,14),(2,6),(2,7),(3,9),(3,10),(4,9),(4,11),(5,2),(5,10),(5,11),(6,13),(7,13),(7,14),(9,1),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(12,14),(13,8),(14,8)],15)=>([(0,3),(0,4),(1,10),(2,7),(2,9),(3,2),(3,11),(3,12),(4,1),(4,11),(4,12),(5,14),(6,14),(7,13),(8,5),(8,13),(9,6),(9,13),(10,5),(10,6),(11,7),(11,8),(12,8),(12,9),(12,10),(13,14)],15)
[6,3,5,2,4,1]=>[4,5,6,2,3,1]=>([(0,3),(0,4),(0,5),(1,13),(2,6),(2,7),(2,14),(3,9),(3,10),(4,9),(4,11),(5,2),(5,10),(5,11),(6,12),(7,12),(7,13),(9,1),(9,14),(10,6),(10,14),(11,7),(11,14),(12,8),(13,8),(14,12),(14,13)],15)=>([(0,3),(0,4),(1,9),(1,14),(2,10),(3,1),(3,7),(3,11),(4,2),(4,7),(4,11),(5,13),(6,13),(7,8),(7,14),(8,5),(8,12),(9,6),(9,12),(10,5),(10,6),(11,8),(11,9),(11,10),(11,14),(12,13),(14,12)],15)
[6,4,3,1,5,2]=>[3,4,6,5,1,2]=>([(0,3),(0,4),(0,5),(1,6),(1,9),(2,7),(2,8),(3,1),(3,11),(3,13),(4,2),(4,12),(4,13),(5,11),(5,12),(6,15),(7,16),(8,15),(8,16),(9,15),(9,16),(11,9),(11,14),(12,7),(12,14),(13,6),(13,8),(13,14),(14,15),(14,16),(15,10),(16,10)],17)=>([(0,3),(0,4),(1,7),(1,13),(2,6),(2,9),(3,2),(3,10),(3,11),(3,12),(4,1),(4,10),(4,11),(4,12),(5,16),(6,14),(7,15),(8,5),(8,15),(9,5),(9,14),(10,6),(10,13),(11,7),(11,8),(12,8),(12,9),(12,13),(13,14),(13,15),(14,16),(15,16)],17)
[6,4,5,2,3,1]=>[3,5,2,6,4,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,18),(1,19),(2,10),(2,13),(2,19),(2,20),(3,9),(3,13),(3,18),(3,20),(4,12),(4,14),(4,18),(4,19),(4,20),(5,11),(5,14),(5,18),(5,19),(5,20),(6,8),(6,9),(6,10),(6,11),(6,12),(8,21),(8,22),(9,15),(9,21),(9,25),(10,15),(10,22),(10,25),(11,16),(11,21),(11,22),(11,25),(12,16),(12,21),(12,22),(12,25),(13,15),(13,25),(14,16),(14,17),(14,25),(15,24),(16,23),(16,24),(17,23),(18,17),(18,21),(18,25),(19,17),(19,22),(19,25),(20,17),(20,25),(21,23),(21,24),(22,23),(22,24),(23,7),(24,7),(25,23),(25,24)],26)=>([(0,3),(0,4),(1,7),(1,13),(1,14),(2,8),(2,15),(2,16),(2,17),(3,1),(3,6),(3,9),(3,10),(3,11),(4,2),(4,6),(4,9),(4,10),(4,11),(5,12),(5,22),(6,15),(6,18),(6,19),(7,20),(7,21),(8,20),(8,21),(8,23),(8,24),(9,5),(9,14),(9,17),(9,18),(9,19),(10,5),(10,13),(10,16),(10,18),(10,19),(11,7),(11,8),(11,13),(11,14),(11,15),(11,16),(11,17),(11,18),(11,19),(12,25),(13,20),(13,22),(14,21),(14,22),(15,23),(15,24),(16,12),(16,20),(16,23),(16,24),(17,12),(17,21),(17,23),(17,24),(18,22),(18,24),(19,22),(19,23),(20,25),(21,25),(22,25),(23,25),(24,25)],26)
[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
[1,2,3,6,5,7,4]=>[1,2,3,7,6,5,4]=>([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)=>([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
[1,2,5,6,4,7,3]=>[1,2,7,6,5,4,3]=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
[1,5,4,6,3,7,2]=>[1,7,6,5,4,3,2]=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)=>([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[4,5,3,7,1,6,2]=>[7,6,5,4,3,1,2]=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
[4,5,3,7,2,6,1]=>[6,7,5,4,3,2,1]=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
[4,6,2,7,1,5,3]=>[7,6,5,4,1,2,3]=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
[4,6,2,7,3,5,1]=>[5,6,7,4,3,2,1]=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
[6,2,4,7,1,3,5]=>[7,6,1,2,3,4,5]=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
[6,2,5,3,7,1,4]=>[7,6,5,1,2,3,4]=>([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)=>([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
[6,2,5,4,1,7,3]=>[4,5,6,7,3,2,1]=>([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)=>([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
[6,5,4,3,1,7,2]=>[3,4,5,6,7,2,1]=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>([(0,1),(0,2),(0,3),(0,4),(1,8),(1,10),(1,12),(1,29),(2,7),(2,10),(2,11),(2,29),(3,7),(3,9),(3,12),(3,29),(4,8),(4,9),(4,11),(4,29),(6,5),(7,17),(7,19),(7,27),(8,18),(8,20),(8,28),(9,17),(9,18),(9,26),(10,19),(10,20),(10,27),(10,28),(11,17),(11,20),(11,26),(11,27),(12,18),(12,19),(12,26),(12,28),(13,14),(13,15),(14,6),(14,16),(15,6),(15,16),(16,5),(17,22),(17,23),(18,22),(18,24),(19,22),(19,23),(19,25),(20,22),(20,24),(20,25),(21,16),(22,21),(23,14),(23,21),(24,15),(24,21),(25,14),(25,15),(25,21),(26,13),(26,23),(26,24),(27,13),(27,23),(27,25),(28,13),(28,24),(28,25),(29,26),(29,27),(29,28)],30)=>([(0,1),(0,2),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,10),(3,11),(3,21),(4,7),(4,8),(4,16),(4,17),(5,9),(5,11),(5,21),(6,9),(6,10),(6,21),(7,13),(7,15),(7,23),(8,14),(8,15),(8,24),(9,18),(9,19),(9,20),(10,7),(10,16),(10,18),(10,20),(11,8),(11,17),(11,19),(11,20),(12,25),(12,26),(12,27),(12,28),(13,25),(13,27),(14,26),(14,28),(15,25),(15,26),(16,13),(16,22),(16,24),(17,14),(17,22),(17,23),(18,12),(18,13),(18,22),(18,23),(19,12),(19,14),(19,22),(19,24),(20,12),(20,15),(20,23),(20,24),(21,16),(21,17),(21,18),(21,19),(22,27),(22,28),(23,26),(23,27),(24,25),(24,28),(25,29),(26,29),(27,29),(28,29)],30)
[5,1,6,2,7,3,8,4]=>[5,6,7,8,1,2,3,4]=>([(0,3),(0,4),(1,6),(1,17),(2,5),(2,16),(3,2),(3,15),(4,1),(4,15),(5,7),(5,12),(6,7),(6,13),(7,18),(9,8),(10,9),(10,19),(11,9),(11,19),(12,10),(12,18),(13,11),(13,18),(14,10),(14,11),(15,16),(15,17),(16,12),(16,14),(17,13),(17,14),(18,19),(19,8)],20)=>([(0,3),(0,4),(1,2),(1,18),(1,19),(2,6),(2,7),(3,16),(3,17),(4,1),(4,16),(4,17),(6,9),(7,8),(8,10),(9,11),(10,5),(11,5),(12,14),(12,15),(13,10),(13,11),(14,8),(14,13),(15,9),(15,13),(16,12),(16,18),(17,12),(17,19),(18,7),(18,14),(19,6),(19,15)],20)
[8,4,6,2,7,3,5,1]=>[5,6,7,8,3,4,2,1]=>([(0,5),(0,6),(0,7),(1,10),(2,12),(2,17),(3,4),(3,18),(3,20),(4,9),(4,16),(4,27),(5,14),(5,15),(6,2),(6,15),(6,19),(7,3),(7,14),(7,19),(8,23),(8,25),(9,22),(10,23),(12,1),(12,24),(13,8),(13,26),(14,18),(14,21),(15,12),(15,21),(16,8),(16,22),(16,26),(17,13),(17,24),(18,9),(18,27),(19,17),(19,20),(19,21),(20,13),(20,16),(20,27),(21,24),(21,27),(22,25),(23,11),(24,10),(24,26),(25,11),(26,23),(26,25),(27,22),(27,26)],28)=>([(0,5),(0,6),(1,3),(1,19),(2,4),(2,17),(2,27),(3,16),(4,13),(4,21),(5,1),(5,12),(5,18),(6,2),(6,12),(6,18),(7,23),(8,24),(9,11),(9,20),(10,8),(10,23),(11,7),(11,22),(12,9),(12,27),(13,14),(13,26),(14,8),(14,25),(15,10),(15,14),(15,22),(16,7),(16,10),(17,13),(17,15),(17,20),(17,21),(18,9),(18,17),(18,19),(18,27),(19,11),(19,15),(19,16),(20,22),(20,26),(21,26),(22,23),(22,25),(23,24),(25,24),(26,25),(27,20),(27,21)],28)
[5,1,7,3,8,4,6,2]=>[5,6,7,8,1,4,3,2]=>([(0,6),(0,7),(0,8),(1,10),(2,12),(2,27),(3,14),(3,18),(4,5),(4,19),(4,22),(5,2),(5,9),(5,21),(6,15),(6,16),(7,3),(7,16),(7,20),(8,4),(8,15),(8,20),(9,27),(10,28),(11,28),(11,29),(12,28),(12,29),(14,1),(14,26),(15,19),(15,23),(16,14),(16,23),(17,11),(17,24),(18,17),(18,26),(19,9),(19,25),(20,18),(20,22),(20,23),(21,11),(21,12),(21,27),(22,17),(22,21),(22,25),(23,25),(23,26),(24,28),(24,29),(25,24),(25,27),(26,10),(26,24),(27,29),(28,13),(29,13)],30)=>([(0,5),(0,6),(1,3),(1,21),(2,16),(2,29),(3,17),(4,2),(4,8),(4,19),(4,22),(5,4),(5,11),(5,12),(5,20),(6,1),(6,11),(6,12),(6,20),(7,28),(8,29),(9,23),(10,7),(10,27),(11,14),(11,22),(12,8),(12,22),(13,9),(13,25),(14,13),(14,26),(15,7),(15,23),(16,10),(16,24),(17,9),(17,15),(18,10),(18,15),(18,25),(19,16),(19,18),(19,26),(20,14),(20,19),(20,21),(21,13),(21,17),(21,18),(22,26),(22,29),(23,28),(24,27),(25,23),(25,27),(26,24),(26,25),(27,28),(29,24)],30)
[7,3,5,1,8,4,6,2]=>[5,6,7,8,3,4,1,2]=>([(0,4),(0,5),(0,6),(1,10),(2,3),(2,16),(2,17),(3,8),(3,9),(3,27),(4,2),(4,14),(4,15),(5,12),(5,13),(5,15),(6,12),(6,13),(6,14),(7,1),(7,24),(8,20),(8,21),(9,20),(9,21),(9,26),(10,23),(12,7),(12,18),(13,7),(13,19),(14,17),(14,18),(14,19),(15,16),(15,18),(15,19),(16,9),(16,22),(16,27),(17,8),(17,22),(17,27),(18,22),(18,24),(19,24),(19,27),(20,23),(20,25),(21,25),(22,21),(22,26),(23,11),(24,10),(24,26),(25,11),(26,23),(26,25),(27,20),(27,26)],28)=>([(0,4),(0,5),(1,13),(2,1),(2,15),(3,6),(3,9),(3,18),(4,2),(4,14),(4,16),(5,3),(5,14),(5,16),(6,17),(6,19),(7,20),(7,21),(8,20),(8,21),(9,12),(9,17),(9,22),(10,11),(10,17),(10,19),(10,22),(11,7),(11,23),(11,24),(12,8),(12,23),(12,24),(13,7),(13,8),(14,6),(14,10),(14,18),(15,11),(15,12),(15,13),(16,9),(16,10),(16,15),(16,18),(17,24),(17,27),(18,19),(18,22),(19,27),(20,26),(21,26),(22,23),(22,27),(23,20),(23,25),(24,21),(24,25),(25,26),(27,25)],28)
[8,4,7,3,6,2,5,1]=>[5,6,7,8,2,3,4,1]=>([(0,5),(0,6),(0,7),(1,20),(2,11),(2,16),(3,4),(3,17),(3,19),(4,9),(4,15),(4,26),(5,12),(5,13),(6,2),(6,13),(6,18),(7,3),(7,12),(7,18),(8,22),(9,20),(9,24),(11,1),(11,26),(12,17),(12,21),(13,11),(13,21),(14,8),(14,27),(15,8),(15,24),(15,27),(16,14),(16,26),(17,9),(17,23),(18,16),(18,19),(18,21),(19,14),(19,15),(19,23),(20,25),(21,23),(21,26),(22,10),(23,24),(23,27),(24,22),(24,25),(25,10),(26,20),(26,27),(27,22),(27,25)],28)=>([(0,4),(0,5),(1,14),(2,10),(2,20),(3,1),(3,11),(3,18),(4,2),(4,17),(4,19),(5,3),(5,17),(5,19),(6,27),(7,21),(8,9),(8,25),(9,6),(9,26),(10,12),(10,24),(11,8),(11,22),(12,7),(12,23),(13,6),(13,21),(14,7),(14,13),(15,8),(15,16),(15,24),(16,9),(16,13),(16,23),(17,11),(17,15),(17,20),(18,12),(18,14),(18,16),(18,22),(19,10),(19,15),(19,18),(19,20),(20,22),(20,24),(21,27),(22,25),(23,21),(23,26),(24,23),(24,25),(25,26),(26,27)],28)
[6,2,7,3,5,1,8,4]=>[5,6,7,8,3,2,1,4]=>([(0,6),(0,7),(0,8),(1,10),(2,12),(2,27),(3,14),(3,18),(4,5),(4,19),(4,22),(5,2),(5,9),(5,21),(6,15),(6,16),(7,3),(7,16),(7,20),(8,4),(8,15),(8,20),(9,27),(10,28),(11,28),(11,29),(12,28),(12,29),(14,1),(14,26),(15,19),(15,23),(16,14),(16,23),(17,11),(17,24),(18,17),(18,26),(19,9),(19,25),(20,18),(20,22),(20,23),(21,11),(21,12),(21,27),(22,17),(22,21),(22,25),(23,25),(23,26),(24,28),(24,29),(25,24),(25,27),(26,10),(26,24),(27,29),(28,13),(29,13)],30)=>([(0,5),(0,6),(1,3),(1,21),(2,16),(2,29),(3,17),(4,2),(4,8),(4,19),(4,22),(5,4),(5,11),(5,12),(5,20),(6,1),(6,11),(6,12),(6,20),(7,28),(8,29),(9,23),(10,7),(10,27),(11,14),(11,22),(12,8),(12,22),(13,9),(13,25),(14,13),(14,26),(15,7),(15,23),(16,10),(16,24),(17,9),(17,15),(18,10),(18,15),(18,25),(19,16),(19,18),(19,26),(20,14),(20,19),(20,21),(21,13),(21,17),(21,18),(22,26),(22,29),(23,28),(24,27),(25,23),(25,27),(26,24),(26,25),(27,28),(29,24)],30)
[6,3,8,1,4,7,2,5]=>[8,7,6,1,2,3,4,5]=>([(0,6),(0,7),(1,4),(1,16),(2,5),(2,15),(3,13),(4,12),(5,3),(5,19),(6,1),(6,17),(7,2),(7,17),(9,11),(10,8),(11,8),(12,9),(13,10),(14,9),(14,18),(15,14),(15,19),(16,12),(16,14),(17,15),(17,16),(18,10),(18,11),(19,13),(19,18)],20)=>([(0,6),(0,7),(1,4),(1,16),(2,5),(2,15),(3,13),(4,12),(5,3),(5,19),(6,1),(6,17),(7,2),(7,17),(9,11),(10,8),(11,8),(12,9),(13,10),(14,9),(14,18),(15,14),(15,19),(16,12),(16,14),(17,15),(17,16),(18,10),(18,11),(19,13),(19,18)],20)
[8,4,5,1,7,3,6,2]=>[5,6,7,8,4,3,1,2]=>([(0,5),(0,6),(0,7),(1,10),(2,12),(2,17),(3,4),(3,18),(3,20),(4,9),(4,16),(5,13),(5,14),(6,2),(6,14),(6,19),(7,3),(7,13),(7,19),(8,24),(8,26),(9,23),(10,24),(12,1),(12,22),(13,18),(13,21),(14,12),(14,21),(15,8),(15,27),(16,8),(16,23),(17,15),(17,22),(18,9),(18,25),(19,17),(19,20),(19,21),(20,15),(20,16),(20,25),(21,22),(21,25),(22,10),(22,27),(23,26),(24,11),(25,23),(25,27),(26,11),(27,24),(27,26)],28)=>([(0,5),(0,6),(1,2),(1,21),(2,17),(3,4),(3,15),(3,19),(4,9),(4,13),(5,1),(5,16),(5,20),(6,3),(6,16),(6,20),(7,27),(8,23),(9,24),(10,7),(10,26),(11,14),(11,22),(12,7),(12,23),(13,10),(13,24),(14,8),(14,25),(15,9),(15,22),(16,11),(16,15),(17,8),(17,12),(18,10),(18,12),(18,25),(19,13),(19,18),(19,22),(20,11),(20,19),(20,21),(21,14),(21,17),(21,18),(22,24),(22,25),(23,27),(24,26),(25,23),(25,26),(26,27)],28)
[6,2,5,1,7,3,8,4]=>[5,6,7,8,2,1,3,4]=>([(0,6),(0,7),(0,8),(1,27),(2,10),(2,27),(3,13),(3,17),(4,5),(4,18),(4,21),(5,2),(5,12),(5,20),(6,15),(6,16),(7,3),(7,16),(7,19),(8,4),(8,15),(8,19),(9,28),(10,28),(10,29),(12,24),(12,27),(13,1),(13,23),(14,9),(14,26),(15,18),(15,22),(16,13),(16,22),(17,14),(17,23),(18,12),(18,25),(19,17),(19,21),(19,22),(20,9),(20,10),(20,24),(21,14),(21,20),(21,25),(22,23),(22,25),(23,26),(23,27),(24,28),(24,29),(25,24),(25,26),(26,28),(26,29),(27,29),(28,11),(29,11)],30)=>([(0,4),(0,5),(1,16),(2,11),(2,22),(3,1),(3,8),(3,12),(3,20),(4,2),(4,15),(4,19),(4,21),(5,3),(5,15),(5,19),(5,21),(6,28),(7,23),(8,24),(9,10),(9,27),(10,6),(10,29),(11,14),(11,26),(12,9),(12,24),(13,6),(13,23),(14,7),(14,25),(15,8),(15,22),(16,7),(16,13),(17,9),(17,18),(17,26),(18,10),(18,13),(18,25),(19,12),(19,17),(19,22),(20,14),(20,16),(20,18),(21,11),(21,17),(21,20),(22,24),(22,26),(23,28),(24,27),(25,23),(25,29),(26,25),(26,27),(27,29),(29,28)],30)
[5,1,6,2,8,4,7,3]=>[5,6,7,8,1,2,4,3]=>([(0,6),(0,7),(0,8),(1,27),(2,10),(2,27),(3,13),(3,17),(4,5),(4,18),(4,21),(5,2),(5,12),(5,20),(6,15),(6,16),(7,3),(7,16),(7,19),(8,4),(8,15),(8,19),(9,28),(10,28),(10,29),(12,24),(12,27),(13,1),(13,23),(14,9),(14,26),(15,18),(15,22),(16,13),(16,22),(17,14),(17,23),(18,12),(18,25),(19,17),(19,21),(19,22),(20,9),(20,10),(20,24),(21,14),(21,20),(21,25),(22,23),(22,25),(23,26),(23,27),(24,28),(24,29),(25,24),(25,26),(26,28),(26,29),(27,29),(28,11),(29,11)],30)=>([(0,4),(0,5),(1,16),(2,11),(2,22),(3,1),(3,8),(3,12),(3,20),(4,2),(4,15),(4,19),(4,21),(5,3),(5,15),(5,19),(5,21),(6,28),(7,23),(8,24),(9,10),(9,27),(10,6),(10,29),(11,14),(11,26),(12,9),(12,24),(13,6),(13,23),(14,7),(14,25),(15,8),(15,22),(16,7),(16,13),(17,9),(17,18),(17,26),(18,10),(18,13),(18,25),(19,12),(19,17),(19,22),(20,14),(20,16),(20,18),(21,11),(21,17),(21,20),(22,24),(22,26),(23,28),(24,27),(25,23),(25,29),(26,25),(26,27),(27,29),(29,28)],30)
[8,4,5,1,6,2,7,3]=>[5,6,7,8,4,1,2,3]=>([(0,5),(0,6),(0,7),(1,22),(2,11),(2,17),(3,4),(3,16),(3,19),(4,9),(4,15),(5,12),(5,13),(6,2),(6,13),(6,18),(7,3),(7,12),(7,18),(8,26),(9,21),(9,22),(11,1),(11,24),(12,16),(12,20),(13,11),(13,20),(14,8),(14,25),(15,8),(15,21),(16,9),(16,23),(17,14),(17,24),(18,17),(18,19),(18,20),(19,14),(19,15),(19,23),(20,23),(20,24),(21,26),(21,27),(22,27),(23,21),(23,25),(24,22),(24,25),(25,26),(25,27),(26,10),(27,10)],28)=>([(0,4),(0,5),(1,16),(2,13),(2,14),(3,1),(3,18),(3,21),(4,2),(4,19),(4,20),(5,3),(5,19),(5,20),(6,27),(7,23),(8,24),(9,6),(9,26),(10,6),(10,23),(11,9),(11,24),(12,7),(12,25),(13,12),(13,22),(14,8),(14,22),(15,11),(15,17),(15,22),(16,7),(16,10),(17,9),(17,10),(17,25),(18,8),(18,11),(19,14),(19,15),(19,18),(20,13),(20,15),(20,21),(21,12),(21,16),(21,17),(22,24),(22,25),(23,27),(24,26),(25,23),(25,26),(26,27)],28)
[7,3,6,2,8,4,5,1]=>[5,6,7,8,4,3,2,1]=>([(0,6),(0,7),(1,4),(1,16),(2,5),(2,15),(3,13),(4,12),(5,3),(5,19),(6,1),(6,17),(7,2),(7,17),(9,11),(10,8),(11,8),(12,9),(13,10),(14,9),(14,18),(15,14),(15,19),(16,12),(16,14),(17,15),(17,16),(18,10),(18,11),(19,13),(19,18)],20)=>([(0,6),(0,7),(1,4),(1,16),(2,5),(2,15),(3,13),(4,12),(5,3),(5,19),(6,1),(6,17),(7,2),(7,17),(9,11),(10,8),(11,8),(12,9),(13,10),(14,9),(14,18),(15,14),(15,19),(16,12),(16,14),(17,15),(17,16),(18,10),(18,11),(19,13),(19,18)],20)
          
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
Map
pattern poset
Description
The pattern poset of a permutation.
This is the poset of all non-empty permutations that occur in the given permutation as a pattern, ordered by pattern containment.
Map
dual poset
Description
The dual of a poset.
The dual (or opposite) of a poset $(\mathcal P,\leq)$ is the poset $(\mathcal P^d,\leq_d)$ with $x \leq_d y$ if $y \leq x$.